A New Model Reduction Method for Nonlinear Dynamical Systems Using Singular PDE Theory

摘要: In the present research study a new approach to problem of modelreduction for nonlinear dynamical systems is proposed. The formulation conveniently realized through system singular quasi-linear invariance PDEs, and an explicit set conditions solvability derived. particular, within class real analytic solutions, aforementioned shown guarantee existence uniqueness locally solution, which then proven represent slow invariant manifold under consideration. As result, exact reduced-order model dynamics obtained restriction original on manifold. local analyticity property solution’s graph that corresponds system’s enables development series solution method, allows polynomial approximation “slow” up desired degree accuracy.